Renormalization of Einstein-Gauss-Bonnet AdS gravity

TL;DR

This paper develops a holographic renormalization framework for Einstein-Gauss-Bonnet AdS gravity, providing finite action and stress-energy tensor calculations in various dimensions, and applies it to analyze six-dimensional black holes.

Contribution

It introduces a covariant counterterm formulation for Einstein-Gauss-Bonnet AdS gravity in six dimensions and compares it with standard methods, ensuring consistent holographic stress tensors.

Findings

Finite asymptotic charges for 6D black holes are obtained.

Black hole thermodynamics is correctly recovered using both renormalization schemes.

The covariant counterterm approach yields consistent results with standard methods.

Abstract

The asymptotic analysis for the metric of a generic solution of Einstein-Gauss-Bonnet AdS theory is provided by solving the field equations in the Fefferman-Graham frame. Using standard holographic renormalization, the counterterms that render the action finite are found up to seven spacetime dimensions. In the case of 6D, an equivalent formulation that permits a fully covariant determination of the counterterms is introduced, based on the finiteness of conformal invariants. It is shown that both schemes end up in the same holographic stress-energy tensor. Physical properties of six-dimensional topological Boulware-Deser black holes in Einstein-Gauss-Bonnet-AdS$_6$ gravity, whose boundary has nontrivial conformal features, are worked out in detail. Employing both renormalization prescriptions, finite asymptotic charges are found, and the correct black hole thermodynamics is recovered.